Math Question

From the formula for a geometric series, the sum is 19/3.

Let \(r\) be the positive real solution to \(x^3 + \dfrac{2}{5} x - 1 = 0\).
Find the exact numerical value of \(r^2 + 2r^5 + 3r^8 + 4r^{11} + \dotsb\) .

answer see: https://web2.0calc.com/questions/math-question_148#r2